Sources of Noncausality

Touchstone data come from three different sources: from measurements, from field solvers (2-D, 3-D, or 2.5-D), and from circuit solvers. Any of these sources can introduce noncausality into data. This technical note analyzes causality issues in data from field solvers and circuit solvers.

Causality Issues with Field Solvers

There are many sources of noncausality in data from field solvers.

• Subsystems in field solvers can have noncausal models.
• Discontinuity of the field solutions can produce noncausal data. Field solvers typically use a special formulation for low-frequency solutions (near DC), which can be discontinuous with the solutions obtained at higher frequencies with the standard formulations.
• Noncausal interpolating functions during interpolation sweep are a frequent source of problems.
• Constant loss-tangent models for modeling frequency-dependent dielectric behavior often contributed to noncausality in the data. Fortunately, the Debye and Djordevic-Sarkar models for dielectric constants have eliminated this source of noncausality.

Causality Issues with Circuit Solvers

Circuit solvers can introduce noncausality into Touchstone data. Most of the noncausality comes from components meant to work at radio or microwave frequencies. A typical example of such a component is the coaxial cable transmission line model. The dielectric loss of the lines is still modeled by constant loss-tangent models (conductance is made to vary linearly with frequency, while capacitance is held constant), and the conductor loss is modeled by varying the square root of the frequency while making the inductance constant with frequency.